A and B both spend `30%` of their income together which is equal to Rs. 26400. If income of A is `20%` more than that of B, then find the income of B (in Rs.)?

Options

A. 52000
B. 48000
C. 40000
D. 36000

Answer

To find the income of B, let's break down the problem step by step.

**Step 1: Understand the total expenditure of A and B**
A and B together spend 30% of their income, which equals Rs. 26,400.

**Step 2: Set up the equation for total income**
Let the total income of A and B be denoted as \( D \). According to the information given:
\[ 0.30D = 26,400 \]

**Step 3: Solve for total income \( D \)**
To find \( D \), we can rearrange the equation:
\[ D = \frac{26,400}{0.30} \]
Calculating this gives:
\[ D = 88,000 \]

**Step 4: Set up the relationship between A's and B's income**
We know that A's income is 20% more than B's income. If we let B's income be \( x \), then A's income can be expressed as:
\[ A = x + 0.20x = 1.20x \]

**Step 5: Express total income in terms of \( x \)**
The total income \( D \) can also be expressed as the sum of A's and B's incomes:
\[ D = A + B = 1.20x + x = 2.20x \]

**Step 6: Set up the equation with the total income**
Now we can set this equal to the total income we calculated:
\[ 2.20x = 88,000 \]

**Step 7: Solve for \( x \) (income of B)**
To find \( x \), we divide both sides by 2.20:
\[ x = \frac{88,000}{2.20} \]
Calculating this gives:
\[ x = 40,000 \]

Thus, the income of B is Rs. 40,000.

### Summary of the Solution:
- Total income \( D = 88,000 \)
- Income of B \( x = 40,000 \)